A Collection of Cubing Curiosities

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The standard T-perm RUR'U'R'FR2U'R'U'RUR'F' with R/R' replaced by r/r' is an A-perm. This is (probably) useless for speedsolving, but it's interesting nonetheless. The purpose of this page is to collect and preserve these cubing curiosities, which until now have existed as "folklore" with no proper home.

Considered for inclusion are
* Interesting algorithms, fingertricks, or ideas on the 3x3 orother twisty puzzles, not necessarily of any practical use, and especially oddities applying to one or very few cases and with no obvious explanation
* Anything else relating more or less to the cube itself that is particularly interesting.

Please send suggestions to the author, with attribution (name and date) when known.

(R U R' U' y)7 is a nice pattern and can also be created by getting four center-edge pairs into one slice and turning it ([R B L R' F R : E]) or getting four corner-edge pairs into one layer and turning it ([R B L R' F R : D] U'). Note that the setup R B L R' F R is the same for both (never realized that until right now...).

Also popularized by Chris: The number of unsolved states of a 3x3x3 is prime.

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Ooooh, Lucas that reminds me! The number of unsolved states of the 8x8x8 and 11x11x11 are also prime numbers (3+8=11 is how I remember that). I'll send that off to Macky, if someone hasn't sent it already.

This is definitely a curiosity - the "31 club" in FMC... A surprisingly large number of famous/important cubers have 31 moves as their official personal best. The current list includes Dan Cohen, Gilles Roux *and* Lars Petrus, Lucas Garron and me, Mike Hughey, Stefan Pochmann, and Yu Nakajima. (And it was the NAR twice )

This is definitely a curiosity - the "31 club" in FMC... A surprisingly large number of famous/important cubers have 31 moves as their official personal best. The current list includes Dan Cohen, Gilles Roux *and* Lars Petrus, Lucas Garron and me, Mike Hughey, Stefan Pochmann, and Yu Nakajima. (And it was the NAR twice )

Even if we could ignore all edges and centres, there's nothing better afaik

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Again seems borderline for the same reason. I'll wait on inclusion for now.

But more importantly, ", which preserves CO," should read "that preserves CO" (without commas). With that kind of grammar, how's a non-cuber to know that not every diagonal corner swap on a 3x3 preserves CO?

cmowla said:

[snip]

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I don't see how anything you wrote is particularly surprising or beautiful. The derivations are impressive but don't seem miraculous in any way. The formulas are some ugly mess that follow by basic combinatorial considerations.

Could you clarify this? Of course God's number for LL is some number. Is it that there's a single case (up to some appropriate equivalence) with this distance? That might not be that surprising. Is it that, for this single case, there's a single algorithm (again up to equivalence) of length 16?

Also, I'm not so sure about some of your attributions. But maybe I'm just jealous I didn't suggest them first.

Regarding Hardwick's conjecture: I checked up to n=54 over four years ago when Chris brought up the n=3 constant; see this post; I don't recall Michael posting on this, but maybe I'm just missing something.

I've been showing people the RU-gen S'U2SU2 for years, although I just consider it common knowledge.
One other interesting variant (I use it all the time during BLD) is R2 U R U R2' U' R' U' R' U2 R'.

In a similar vein, an Mu-gen U-perm where all the M-moves and all the u-moves can naturally go in the same direction each time: M2 u' M' u2' M' u' M2'

From an email to you (Macky) on June 4:

There are 5 (RU-gen) F2L cases where the corner is facing up. Four of these have very nice algs, while the fifth somehow does not. Moreover, each of the four algs is its own self-inverse (by permutation), and preserves the orientation of all other LL pieces. I think that's pretty curious; I can partially of explain it from the algs, but I don't quite see why it should work out this way.

Again seems borderline for the same reason. I'll wait on inclusion for now.

But more importantly, ", which preserves CO," should read "that preserves CO" (without commas). With that kind of grammar, how's a non-cuber to know that not every diagonal corner swap on a 3x3 preserves CO?

Click to expand...

Sorry, I couldn't really find a nice and easy to understand way of describing this "oddity", thanks. I'm never sure when to use "which" or "that"...

Could you clarify this? Of course God's number for LL is some number. Is it that there's a single case (up to some appropriate equivalence) with this distance? That might not be that surprising. Is it that, for this single case, there's a single algorithm (again up to equivalence) of length 16?

Click to expand...

Ah sorry. I thought Rinfiyks meant this is the only LL case that requires 16 moves to solve and all of the other LL cases require a maximum of 15 moves. I don't actually know myself.